Question: Multiply the following complex numbers: $({5-5i}) \cdot ({-3+5i})$
Answer: Complex numbers are multiplied like any two binomials. First use the distributive property: $ ({5-5i}) \cdot ({-3+5i}) = $ $ ({5} \cdot {-3}) + ({5} \cdot {5}i) + ({-5}i \cdot {-3}) + ({-5}i \cdot {5}i) $ Then simplify the terms: $ (-15) + (25i) + (15i) + (-25 \cdot i^2) $ Imaginary unit multiples can be grouped together. $ -15 + (25 + 15)i - 25i^2 $ After we plug in $i^2 = -1$ , the result becomes $ -15 + (25 + 15)i - (-25) $ The result is simplified: $ (-15 + 25) + (40i) = 10+40i $